Random number generator based on turbulent convection

ABSTRACT

A method for generating random numbers includes the steps of providing a liquid crystal cell containing a liquid crystal material, wherein a potential difference is applied across said liquid crystal material to cause a chaotic turbulent flow. The resulting flow or physical result of the liquid crystal material is measured to generate a baseline measurement, and subsequently the at least one physical property is measured again to generate a plurality of reading measurements. Determining the difference between each of the reading measurements and the baseline measurement, and setting bits based on the differences generates a sequence of random numbers. An apparatus for generating random numbers is also disclosed. These truly random numbers may then be used to encrypt data prior to transmission.

[0001] This application claims benefit of pending U.S. ProvisionalApplication Ser. No. 60/183,447 filed on Feb. 18, 2000.

TECHNICAL FIELD

[0002] This invention relates to generating truly random numbers. Randomnumbers are essential in generating “keys” for strong data encryption.Specifically, this invention relates to the use of nonlinearamplification of noise that is produced when a liquid is undergoingturbulent flow, to produce truly random numbers. More specifically, thisinvention relates to the use of nematic liquid crystals; that whensubject to sufficiently strong electric fields, a spatio-temporallychaotic flow spontaneously forms. Under these circumstances,fluctuations in physical properties such as the light transmissivity ofthe liquid crystal are completely random, uncorrelated andunpredictable. Measurements of these fluctuations yield a stream oftruly random numbers.

BACKGROUND OF THE INVENTION

[0003] The increasing ubiquity of confidential communications via opennetworks has created an urgent need for the strongest possible dataencryption techniques. Modern encryption techniques rely on “keys.” Theencryption is only as strong as the key. If the key can be guessed by anattacker, the encryption is compromised. The less random the process forgenerating the key, the easier it is to guess. It is for this reasonthat generators that can produce truly random numbers are essential fordata security.

[0004] One essential feature in protecting data encryption is the lengthof the key. If a key has few digits, it can be easily guessed, whethergenerated by a random process or not. A key must be changed at intervalsshorter than are necessary to guess the key by exhaustive search. Sincecomputing power is continually reducing the time needed for exhaustivesearching of keys, random number generators must be able to producenumbers at a substantial rate.

[0005] Various prior art exists for generating random numbers. The mostcommon are computer algorithms. While these are the easiest toimplement, they are inherently only “pseudo-random.” That is, they arenot truly random, and often, if one can observe a sequence of numbersgenerated by such an algorithm, it is possible to deduce subsequentnumbers. When more randomness is desired, combinations of differentalgorithms for producing pseudo-random numbers are combined. Otherdevices rely on fundamentally irregular natural processes, such as thethermal noise generated by all electrically resistive elements (Johnsonnoise), or the intrinsic unpredictability of the time between decays ofradioactive nuclei. Both of these have drawbacks. While thermal noise isindeed random, before an actual number can be generated from this noise,it must be significantly amplified by electronic means. The bandwidthcharacteristics of the amplifier then play a significant role in thepredictability of the resulting stream of numbers. Measuring the timingof radioactive nuclei requires special equipment to detect the decayproducts, and of course, whenever ionizing radiation is employed, thereare safety concerns.

[0006] What is needed therefore is a random number generating devicethat quickly produces a sequence of numbers. This sequence must beentirely unpredictable. That is, even if one has knowledge of the firstn members of this sequence (for any value of n), subsequent members ofthe sequence, beyond n, cannot be predicted. Moreover, this deviceshould be easily hybridized with traditional semiconductor technology sothat it can be straightforwardly incorporated into computing andcommunication equipment.

SUMMARY OF INVENTION

[0007] It is therefore an aspect of the present invention to provide amethod and apparatus for generating truly random numbers.

[0008] It is yet another aspect of this invention to provide a methodand apparatus, as set forth above, wherein data is encrypted using trulyrandom numbers.

[0009] It is still yet another aspect of the present invention toprovide a liquid crystal cell which includes a pair of opposedsubstrates having electrodes facing each of the substrates and wherein aliquid crystal material is disposed therebetween.

[0010] It is a further aspect of the present invention to provide amethod and apparatus, as set forth above, wherein a physical stimulussuch as a voltage is applied to the liquid crystal cell to force theliquid crystal material into chaotic, turbulent behavior.

[0011] It is yet a further aspect of the present invention to provide amethod and apparatus, as set forth above, wherein a physical property ofthe liquid crystal material is measured after application of thephysical stimulus and wherein these physical properties could beabsorbence, transmittance, or reflectance values of the light ormeasurement of current flow or any other similar physical property thatcan be readily measured.

[0012] Still yet another aspect of the present invention is to provide amethod and apparatus, as set forth above, wherein comparisons are madebetween a baseline measurement and subsequent measurements of thephysical property to generate a plurality of bits which are in turnemployed to generate a random number, wherein these random numbers maybe used to encrypt transmitted data.

[0013] It is still yet another aspect of the present invention toprovide a method and apparatus, as set forth above, wherein a resultingvoltage value applied to the liquid crystal material results in avoltage-to-current conversion which is filtered and received by adigital-to-analog convertor for further processing as either thebaseline measurement or a subsequent measurement for comparison to thebaseline measurement.

[0014] The foregoing and other aspects of the present invention whichshall become apparent as the detailed description proceeds, are achievedby a method for generating random numbers comprising providing a liquidcrystal cell containing a liquid crystal material between substrates,each substrate having a facing electrode, applying a potentialdifference across the electrodes, measuring at least one physicalproperty of the liquid crystal material to generate a plurality ofreading measurements, and setting bits based on the plurality of readingmeasurements to generate a sequence of random numbers.

[0015] Other aspects of the present invention are attained by anapparatus for the generation of random numbers comprising a pair ofopposed substrates containing a layer of liquid crystal therebetweeneach the substrate having an electrode facing the other the substrates,a power supply applying an electric potential across the electrodes todrive the liquid crystal into a chaotic flow, at least one device formeasuring a physical property of the layer of liquid crystal whichgenerates physical property measurements after an electric potential isapplied, and an interface in communication with the device for measuringa physical property, wherein the interface digitizes the physicalproperty measurements to generate a random number.

[0016] Still another aspect of the present invention is attained by amethod of encrypting data comprising providing a liquid crystal cellresponsive to an electrical stimulus, applying an electrical stimulus tothe liquid crystal cell, measuring at least one physical property of theliquid crystal cell to generate a baseline measurement, setting aplurality of bits based on the baseline measurement so as to generate asequence of random numbers, using the sequence of random numbers togenerate an encryption key.

[0017] By generating truly random numbers, the present invention enablesdata to be encrypted using truly random numbers. Such encryption may beaccomplished by a computer or a computer network which is equipped withthe apparatus of the present invention. The apparatus, when incorporatedinto a computer, may be a peripheral computer device or it may beincorporated into the computer as a whole. The present invention alsoenables a computer program to incorporate encrypted data.

[0018] At least one or more of the foregoing aspects, together with theadvantages thereof over the known art relating to generation of randomnumbers, which shall become apparent from the specification whichfollows, are accomplished by the invention as hereinafter described andclaimed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1 is a schematic representation of a random number generatorapparatus according to the present invention;

[0020]FIG. 2 is a schematic representation of an alternate random numbergenerator apparatus;

[0021]FIG. 3 shows the transmitted light intensity through the liquidcrystal cell of the present invention;

[0022]FIG. 4 shows a histogram of light intensity fluctuations for thisapparatus; and

[0023]FIG. 5 shows the Fourier transform of light intensityfluctuations.

PREFERRED EMBODIMENT FOR CARRYING OUT THE INVENTION

[0024] The present invention is directed to a method and apparatus forthe generation of random numbers based on chaotic, turbulent flow, whichis well known for its random behavior. Such flows are highly nonlinear,in that very many spatial and temporal Fourier modes are stronglycoupled and so are continually mixing. This strong nonlinear couplingmakes the properties of the flow field in the future impossible topredict even with complete knowledge of the past. Another point of viewof this flow is that thermal fluctuations are strongly and nonlinearlyamplified by the coupling of different time and length scales. Whenthese fluctuations are probed and measured, they can form the basis of atruly random number generator, one based on an inherently unpredictablephysical process. Nematic liquid crystals, under appropriate conditions,when subject to a sufficiently strong electric field can be made toundergo turbulent, chaotic flow. This is sometimes referred to asdynamic scattering mode, and formed the basis for early liquid crystaldisplays.

[0025] In general, a series of random numbers is generated by providinga liquid crystal cell, applying a potential difference across the liquidcrystal cell, measuring a physical property of the liquid crystal cellto generate a baseline measurement, subsequently measuring the physicalproperty of the liquid crystal cell to generate a plurality of readingmeasurements, determining the difference between each of the readingmeasurements and the baseline measurement, and setting bits based on thedifferences between the plurality of reading measurements and thebaseline measurement.

[0026] The present invention can be described with reference to FIG. 1which shows a random number generator designated generally by thenumeral 10. Random number generator 10 contains a liquid crystal cell 12which contains a thin layer of nematic or other liquid crystal 14confined between two parallel, transparent substrates 15 each havingfacing plane electrodes 16. Electrodes 16 are electrically connected toa power source 18. Random number generator 10 also contains a lightsource 20 which is disposed on one side of liquid crystal cell 12. Lightsource 20 is also disposed in such a way that light 21 impinges onliquid crystal cell 12 at an angle normal to liquid crystal cell 12. Theangle of light incidence may be altered according to the resulting lightproperty to be measured. A photodetector 22, such as a photodiode, isdisposed on the opposite side of liquid crystal cell 12 from lightsource 20. Photodetector 22 is in communication with a computerinterface 24 for digitizing light intensity measurements. Interface 24may contain the necessary hardware, software and memory to maintain acomputer program for processing these measurements into a continuousstream of random numbers.

[0027] According to the method of this invention, liquid crystal cell 12is in electrical communication with power source 18, inducing liquidcrystal 14 to undergo turbulent, chaotic flow. Light source 20 producescollimated light 21 which impinges on liquid crystal cell 12. Light 21is scattered by liquid crystal 14 in liquid crystal cell 12. Light 21′emerging from liquid crystal cell 12 is detected by photodetector 22.Photodetector 22 converts the light intensity measured to an analogsignal, which is communicated to computer interface 24. Interface 24converts the analog signal to a digital signal. The digital signal maybe converted to a series of random numbers either by interface 24 or bya computer (not shown) in communication with interface 24.

[0028]FIG. 2 shows an alternate embodiment of a random number generatordesignated generally by the numeral 30. Random number generator 30contains a liquid crystal cell 12 which contains a thin layer of nematicor other liquid crystal 14 confined between two parallel, transparentsubstrates 15 each having facing plane electrodes 16. One of theelectrodes 16 is electrically connected to a power source 18. The otherelectrode is connected to a high impedance operational amplifier 32,which is serially connected to a high pass filter 34. The amplifier, inthis instance, is employed as a current-to-voltage converter such asembodied in LF 356BN supplied by National Semiconductor, Inc., of SantaClara, Calif. High pass filter 32 is electrically connected to computerinterface 24, which converts the analog signals into digital, randomnumbers, as described in the first embodiment.

[0029] The apparatus shown in FIG. 2 may be used to generate randomnumbers as described below. Power source 18 supplies an electric currentacross electrodes 16 that induces liquid crystal 14 to undergoturbulent, chaotic flow. The path to ground for the electric currentsupplied by power source 18 that traverses the liquid crystal layer 14is input to amplifier 32. Amplifier 32 converts the current valuereceived from liquid crystal cell 12 to a voltage value, such that thevoltage signal output of amplifier 32 is proportional to the currentthat has passed through liquid crystal 14. This output signal isfiltered by high-pass filter 34 such that only the fluctuations in thecurrent, which now corresponds to the voltage signal output, not itsaverage value, are sampled. The filtered analog signals are thencommunicated to interface 24 through an analog-digital convertor 36which converts the analog signals into digital, random numbers.

[0030] The liquid crystal cell of the present invention may contain anytype of liquid crystal compound provided that it has a sufficientlysmall dielectric constant anisotropy and a sufficiently large electricalconductivity and conductivity anisotropy. Dielectric constant anisotropyis most easily measured by finding the difference in capacitance of theliquid crystal layer under two configurations: when its direction ofmolecular orientation is parallel to the probe electric field used forthe measurement, and when its direction of molecular orientation isperpendicular to the probe electric field. It is believed that if thedielectic constant anistropy is larger than about 0.1 then the devicewill not work as effectively. Conductivity anisotropy is most easilymeasured by finding the difference between the conductance of the liquidcrystal layer under two configurations: when its direction of molecularorientation is parallel to the probe electric field used for themeasurement, and when its direction of molecular orientation isperpendicular to the probe electric field. As long as the conductivityanisotropy is at least greater than zero, the device will likely work.The required potential difference to induce the chaotic flow will getmuch larger as the conductivity anisotropy becomes smaller. Liquidcrystals that do not have an inordinately large viscosity are preferred;a rotational viscosity less than 500 centiPoise is preferred. In orderto raise the electrical conductivity of a liquid crystal compound, asmall quantity of a dopant may be added. It is generally preferred thatthe liquid crystal be doped, choosing both the dopant and the dopantlevel sufficient to produce an electrical conductivity between 10⁻⁶(Ωm)⁻¹ and 10⁻⁸ (Ωm)⁻¹. Any material which dissociates into charged ionswhen dissolved in the liquid crystal compound may be used as a dopant.For example, acceptable dopants include tetrabutyl ammonium bromide(TBAB), iodine, and tetracyanoquinodimethane. Suitable liquid crystalcompounds, to name a few, include a mixture of alkoxy-azobenzenessupplied in the U.S. by EM Industries, Inc., Hawthorne, N.Y., under thetrade name N5, the common name for this in the literature is Phase V;4-ethyl-2-fluoro-4′-[2-(trans-4-pentylcyclohexyl)-ethyl] biphenyl, alsosupplied by EM Industries under the trade name I52. A mixture of phenylbenzoates although not commercially available, could be used. This iscommonly known in the literature as Mischung V. It is composed of 22.0%decyloxyphenyl-hexyloxy benzoate; 30.3% pentyloxyphenyl-octyltoxybenzoate; 13.3% hexyloxyphenyl-heptyloxy benzoate; and 34.4% hexylphenyloctyloxybenzoate. There are many other possible candidates. In oneembodiment, the liquid crystal cell contains nematic liquid crystal.Nematic liquid crystal includes the compoundsN-(pmethoxybenzylidene)-p-butylaniline. (MBBA), among others.

[0031] The liquid crystal cell may be constructed according to methodsknown in the art for liquid crystal cells. The liquid crystal cell mayalso contain components known in the liquid crystal cell art. Forexample, liquid crystal cells may contain an alignment layer on thesurface of the substrates of the cell. Use of an alignment layer isoptional, however, because this invention operates under conditionswhere the liquid crystal is undergoing turbulent flow. Therefore, theboundary conditions on the liquid crystal's direction of averagemolecular orientation are not relevant. When an alignment layer is used,its composition is not critical. Likewise, it is also not necessary touse glass plates as a substrate in the liquid crystal cell. A device maybe constructed using transparent plastic film possessing a conductingcoating. Typically, indium oxide or indium tin oxide (ITO) are used as aconductive coating in liquid crystal cells, although any other materialsuitable for use in a liquid crystal cell may also be used. Theconductive coatings are connected to the electrodes 16 in a manner wellknown in the art.

[0032] The distance between the substrates of the liquid crystal cell,and therefore the thickness of the liquid crystal material, may bevaried according to the needs of a particular application or system andon the physical property to be measured. For example, if lightscattering by the liquid crystal is to measured by measuring lighttransmission through the liquid crystal cell, as described more fullybelow, one thickness may be desired. If this distance is too small, theoptical signal will be weak because the light will not traverse enoughturbulent liquid crystal to be strongly affected. If it is too large,the liquid crystal becomes more opaque, also diminishing the overalloptical signal. If, however, light scattering is to be measured as afunction of light reflected by the liquid crystal a greater thicknessmay be desired Typically, the distance between electrodes may be betweenabout 10 μm and about 100 μm although other thicknesses may be used.

[0033] Consistent with techniques known in the liquid crystal cell art,a potential difference is applied across the liquid crystal cell by anymethod known in the art. Typically, an electric potential is appliedacross two electrodes which are located on either side of the liquidcrystal. The character of the potential difference that is applied isalso not crucial. An alternating current (AC) or direct current (DC)potential may be used, but depending on the properties of the liquidcrystal used, use of a DC potential may lead to undesirable screeningelectric fields or electrochemical reactions. A sine wave or otherperiodic wave form may be used. A square wave potential has theadvantage that the peak value of the potential is the same as the rmsvalue. The frequency of the waveform is not crucial, but the minimumnecessary rms value of the potential difference increases as thefrequency increases.

[0034] As mentioned above, the present invention is based on chaotic,turbulent flow of liquid crystal material. Variations in the physicalproperties of a liquid crystal in such a state are random andnon-predictable. One such property is the scattering of light by theliquid crystal. Light scattering may be measured by light transmissionthrough the liquid crystal or by light absorbance by the liquid crystal.It is also envisioned that light scattering properties may be quantifiedby measuring the amount of light reflected by the liquid crystal. Thelight source is not critical, so long as it is has constant intensity,is fairly collimated and is bright enough to render a measurable signalreceivable by a photodetector. In this instance, collimated does notmean polarized. It means that all the light rays from the source aremore or less parallel, rather than a source where the light is fanningout from a central point. Non-limiting examples of acceptable lightsources include light emitting diodes (LED). An infra-red LED may bedesirable to reduce power consumption.

[0035] The light scattering properties of liquid crystal materialundergoing turbulent, chaotic flow may be detected by a photodiode orphotodetector. The type of photodetector used is not critical, so longas it possesses a response time at least as quick as the desiredsampling rate. The photodector is optionally in communication with asignal amplifier 25. Likewise, the method of amplification of the signalfrom the photodetector is not critical, providing the amplifier'sbandwidth has a flat response from DC to well above the sampling rate.The amplifier should be chosen so that its intrinsic noise is well belowthat of the light intensity fluctuations that it records.

[0036] The amplifier may also be in communication with an analog todigital converter. Any method of analog to digital conversion may beemployed. Indeed, one particularly quick and inexpensive method is touse a comparator as a one-bit analog to digital converter 26. Thistechnique would result in a stream of binary random digital numbers. Inthis case, one would compare the actual light intensity signal with itsaverage value obtained by passing the electrical signal from thephotodiode through a low pass filter with time constant much longer thanthe sampling rate. Other methods of conversion of the light intensity toa digital signal may also be used. One such method involves the use of aphotometer 28 which is in communication with photodetector 22. Theoutput of the photodetector is amplified and converted to a digitalnumber via analog to digital conversion by the photometer. Thephotometer is also in communication and interrogated by a computer viainterface 24. The photometer communicates the digital number to thecomputer, and the computer thus receives to either store or furtherprocess a sequence of random, digital numbers. This stream of randomnumbers will be centered around a number representing the averagetransmitted light intensity. If random numbers centered around zero aredesired, the average transmitted light intensity is subtracted from eachof these numbers. This may be performed either by software, or by accoupling the electrical signal into the photometer through a capacitorin series.

[0037] As mentioned above, light scattering may also be quantified bymeasuring the amount of light reflected by the liquid crystal layerrather than measuring the amount of light transmitted through orabsorbed by a liquid crystal layer. This back-scattering geometry cantherefore be used with liquid crystal layers that are less transmissiveto light, either because they are thicker, or are more opaque becausethe turbulent flow is being driven more violently by a larger potentialdifference than may be used in a light transmission device as describedabove.

[0038] The apparatus of the present invention may be a component ofcomputer or a computer network, either as a peripheral device orintegrated into a computer as a whole. For example, the device may beentirely packaged as one hybrid semiconductor device, for instance formounting directly as a component on a printed circuit board. In thisembodiment, the light source, liquid crystal assembly and photodetectorare held together as a “sandwich,” with the liquid crystal assembly inthe middle. This sandwich is packaged together with an integratedcircuit. The integrated circuit contains devices for and accomplishesthe functions of generating a source of a potential difference acrossthe liquid crystal, amplifying that source, acting as an amplifier forthe signal from the photodetector, and converting the analog signal to adigital signal.

[0039] It is also envisioned that measurements of other physicalproperties that vary randomly under chaotic, turbulent flow in liquidcrystal material may be utilized to generate random numbers. Accordingto one such method, random numbers may be generated entirely from theelectrical response of the liquid crystal layer while it is undergoingturbulent, chaotic flow. In this embodiment, the random numbers aregenerated not by measuring the fluctuations in the amount of lighttransmitted through the liquid crystal, but by measuring thefluctuations in the electrical current traversing the liquid crystal asdescribed above.

[0040] This generator 10, 30 could be a component of computer or acomputer network such as a semiconductor device, which could be mounteddirectly on a circuit board, as also described above. In such a case,the liquid crystal assembly would be packaged together with anintegrated circuit. The integrated circuit would contain devices for andaccomplish the functions of generating a source of a potentialdifference across the liquid crystal, amplifying the current that haspassed through the liquid crystal, converting the current to a voltagesignal, and converting the analog voltage signal to a digital signal.

[0041] It is also envisioned that higher rates of generating randomnumbers may be obtained by multiplexing the apparatus of the presentinvention. Multiplexing may be achieved in the embodiment which utilizeslight scattering properties, for example, by employing multiplephotodetectors positioned at different lateral positions behind theliquid crystal layer. The light received at different photodetectorswill have followed different but parallel paths, laterally displacedfrom one another, through the liquid crystal layer. Since the turbulentflow is incoherent not only temporally but spatially, the fluctuationsin the light intensity as measured along such paths will not becorrelated with one another. Thus, each photodetector is a source forgenerating uncorrelated random numbers, and these sources will beuncorrelated with each other. The numbers generated by thesephotodetectors in parallel with each other can be multiplexed to producea serial stream of number with a generation rate m times higher than canbe achieved with a single photodetector, where m is the number ofphotodetectors used. For this embodiment, one may employ multiple lightsources, but this is not necessary. A single light source thatilluminates the entire liquid crystal layer is sufficient.

[0042] The apparatus of the present invention may be used to generaterandom numbers for creating an encryption key for encoding data. In thisway, the present invention also provides data encrypted using trulyrandom numbers. It also provides a computer program which comprises dataencrypted using truly random numbers.

[0043] The following non-limiting example is provided in order todemonstrate practice of the present invention. The nematic liquidcrystal compound N-(p-methoxybenzylidene)-p-butylaniline. (MBBA) wasdoped by adding 0.0005 wt % tetrabutyl ammonium bromide (TBAB) in orderto yield a larger electrical conductivity than is present in pure MBBA.The liquid crystal compound was then introduced via capillary actioninto a pre-prepared “liquid crystal sample cell” assembly manufacturedby E.H.C. Co. of Tokyo, Japan. This assembly was comprised of two flatsheets of glass, each 1 mm thick. The two sheets of glass were fixed toeach other with adhesive. Interposed between them were glass fiberspacers. These spacers served to maintain the two sheets of glass afixed distance from each other, and parallel to each other. The distancebetween the glass plates was 25 micrometers. A transparent coating ofindium tin oxide (ITO) was deposited upon each sheet of glass. A thinlayer of polyimide polymer coating was deposited on top of the ITO toact as an alignment layer. This polymer coating was unidirectionallyrubbed to induce planar alignment of the liquid crystal optical axis. Asmentioned above, the use of an alignment layer is not essential to theoperation of this invention. In the assembly of the sample cell, the twosheets of glass were positioned so the coated surfaces of the glassfaced each other. The region between these two glass surfaces comprisedthe volume in which the liquid crystal resided. Capillary actionprevented the liquid crystal from leaking out. The sample cell hadaccess for attaching electrical connections to the ITO coated conductiveareas on each sheet of glass. The electrical connections wereaccomplished by affixing thin copper wires to the conducting areas ofeach sheet of glass using electrically conductive silver-filled epoxy.

[0044] These wires were the means of producing a potential differenceacross the thin layer of liquid crystal. The potential difference wasproduced by a function generator adjusted to generate a sine wave outputwith frequency 100 Hz and adjustable amplitude; the voltage signal fromthis device was stepped up using a transformer. The rms value of thepotential difference across the liquid crystal for this reduction topractice was typically 40 V. It is envisioned that the invention'sperformance does not rely critically on the exact value of thispotential difference, so long as the value is somewhat greater than thecritical value required for the DSM1-DSM2 transition, as described in S.Kai and K. Hirakawa, Supplements to Progress in Theoretical Physics, vol64, pp 212-243, 1978, the disclosure of which is hereby incorporated byreference.

[0045] The light source for this example was a 5 mW helium-neon laser.Its light impinged on the liquid crystal sample cell at angle ofincidence normal to the glass plates. The light traversed the samplecell and the liquid crystal contained therein and was dynamically andrandomly scattered by the liquid crystal material. The outgoing,transmitted light was detected by a photodiode detector. The output ofthis photodiode detector was amplified and converted to a digital numbervia analog to digital conversion by a stand-alone photometer. Thephotometer was interrogated at the desired sampling rate over a generalpurpose interface bus (GPIB) by a personal computer. The photometercommunicated the digital number to the computer over the same bus, andthe computer thus received to either store or further process a sequenceof random, digital numbers. This stream of random numbers was centeredaround a number representing the average transmitted light intensity. Itis also envisioned that if random numbers centered around zero aredesired, the average transmitted light intensity may be subtracted fromeach of these numbers. This may be performed either by software, or byAC coupling the electrical signal into the photometer through acapacitor in series.

[0046] The recorded intensity of light transmitted through the liquidcrystal cell described above is shown in FIG. 3. As shown by FIG. 3, thetransmitted light intensity follows no discernable pattern.

[0047]FIG. 4 shows a histogram of light intensity fluctuations for thisdevice, indicating a normal distribution as is expected from the centrallimit theorem.

[0048]FIG. 5 shows a Fourier transform of the light intensityfluctuations, which exhibits no visible structure, indicating a trulyrandom sequence.

[0049] It should be evident that the present invention is highlyeffective in providing a method and apparatus for generating trulyrandom numbers based on turbulent chaotic flow of liquid crystalmaterial. It is, therefore, to be understood that any variations evidentfall within the scope of the claimed invention and thus, the selectionof specific component elements can be determined without departing fromthe spirit of the invention herein disclosed and described.

What is claimed is:
 1. A method for generating random numberscomprising: providing a liquid crystal cell containing a liquid crystalmaterial between substrates, each substrate having a facing electrode;applying a potential difference across said electrodes; measuring atleast one physical property of said liquid crystal material to generatea plurality of reading measurements; and setting bits based on saidplurality of reading measurements to generate a sequence of randomnumbers.
 2. The method of claim 1 , wherein said at least one physicalproperty is selected from the group consisting of light absorbed by theliquid crystal, light transmitted by the liquid crystal, light reflectedby the liquid crystal, and the amount of electric current traversing theliquid crystal.
 3. The method of claim 1 , further comprising firstmeasuring said at least one physical property to generate a baselinemeasurement; subsequently measuring said at least one physical propertyto generate a plurality of reading measurements; and setting said bitsbased on a comparison of said baseline measurement to said plurality ofreading measurements.
 4. The method of claim 1 , wherein said liquidcrystal material comprises nematic liquid crystal.
 5. The method ofclaim 1 , wherein said applying step causes the liquid crystal materialto undergo a chaotic turbulent flow.
 6. The method of claim 1 , whereinsaid at least one physical property comprises a plurality of lightsources directing light toward said liquid crystal cell and a likeplurality of light detectors to measure properties of the light afterimpinging said liquid crystal cell.
 7. An apparatus for the generationof random numbers comprising: a pair of opposed substrates containing alayer of liquid crystal therebetween each said substrate having anelectrode facing the other said substrates; a power supply applying anelectric potential across said electrodes to drive said liquid crystalinto a chaotic flow; at least one device for measuring a physicalproperty of said layer of liquid crystal which generates physicalproperty measurements after an electric potential is applied; and aninterface in communication with said device for measuring a physicalproperty, wherein said interface digitizes said physical propertymeasurements to generate a random number.
 8. The apparatus according toclaim 7 , further comprising: a computer program connected to saidinterface, wherein said computer program processes said digitizedmeasurements into random numbers for use in encrypting data.
 9. Theapparatus according to claim 7 , wherein said layer of liquid crystal isa nematic material.
 10. A method of encrypting data comprising:providing a liquid crystal cell responsive to an electrical stimulus;applying an electrical stimulus to said liquid crystal cell; measuringat least one physical property of said liquid crystal cell to generate abaseline measurement; setting a plurality of bits based on said baselinemeasurement so as to generate a sequence of random numbers; and usingsaid sequence of random numbers to generate an encryption key.
 11. Themethod according to claim 10 , further comprising: applying saidencryption key to data transmitted by a computing device.
 12. The methodaccording to claim 10 further comprising subsequently measuring the atleast one physical property of said liquid crystal cell to generate aplurality of reading measurements; determining the difference betweeneach of said reading measurements and the baseline measurement; andsetting said plurality of bits based on differences between saidplurality of reading measurements and said baseline measurement togenerate said sequence of random numbers.